Let's say, hypothetically, that life has a 1/1,000,000 chance of emerging on a given planet. Obviously it's much less but bear with me. Let's also say that there are 1,000,000,000 planets in Universe X. That means that we have a 1/100 chance of obtaining life in Universe X. That's small enough to where we can bet it just won't happen.
Obviously it's been pointed out that your numbers aren't a good analogy for the number of planets in the universe, but even using them:
If life has a 1/1,000,000 chance of emerging on a given planet then for every planet you have, it's a trial with a success probability of 1/1,000,000 (and failure propability of 1 - 1/1,000,000).
If you have 1,000,000,000 trials, then the probability of at least one success is 1 - probability of zero successes. Probability of zero successes is the probability of 1,000,000,000 failures, i.e. (1 - 1/1,000,000)^1,000,000,000 = approximately zero (shows up as zero on my calculator). So probability of there being one or more planets with life is approximately one, i.e. basically a sure thing.
(For reference, if it was a one in a million chance with a million planets, then probability of there being one or more planets with life would be about 0.63, I think. Since your example made it so likely that the chance of no life had to be rounded to approximately zero).